Algorithm - Mergesort & Quicksort
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1. The document discusses the merge sort and quicksort algorithms. 2. Merge sort works by dividing an array into two halves, sorting each half recursively, and then merging the sorted halves into a single sorted array. 3. Quicksort works by selecting a pivot element and partitioning the array into two halves based on element values relative to the pivot.
![QUICKSORT (A, p, r)
1. if p < r
2. q = PARTITION (A, p, r)
3. QUICKSORT (A, p, q-1)
4. QUICKSORT (A, q -1, r)
Partitioning the array
PARTITION (A, p, r)
1. X=A[r]
2. i =p -1
3. for j = p to r -1
4. if A[j] X
5. i = i + 1
6. exchange A[i] with A[j]
7. exchange A[i+1] with A[r]
8. return i+1](https://image.slidesharecdn.com/algorithm-cse-225-2-150731201937-lva1-app6892/85/Algorithm-Mergesort-Quicksort-42-320.jpg)
Algorithm - Mergesort & Quicksort
- 2. Course title : Algorithm - Mergesort & Quicksort CSE-225 • Submitted By: • Submitted ToName: Istiaque Ahmed Shuvo Id:141311057 5th batch ,5th semester Sec-B Dept. Of Cse Varendra University,rajshahi Name: Atiquer Rahman Sarkar, CSE, Varendra University
- 4. Merge sort Algorithm Merge Sort Merge sort is based on Divide and conquer method. It takes the list to be sorted and divide it in half to create two unsorted lists. The two unsorted lists are then sorted and merged to get a sorted list. The two unsorted lists are sorted by continually calling the merge-sort algorithm; we eventually get a list of size 1 which is already sorted. The two lists of size 1 are then merged. Example sort Example
- 5. The most well known algorithm design strategy: 1.Divide instance of problem into two or more smaller instances 2.Solve smaller instances recursively 3.Obtain solution to original (larger) instance by combining these solutions
- 6. Divide-and-conquer Technique subproblem 2 of size n/2 subproblem 1 of size n/2 a solution to subproblem 1 a solution to the original problem a solution to subproblem 2 a problem of size n
- 7. Divide and Conquer Examples • Sorting: mergesort and quicksort • Tree traversals • Matrix multiplication-Strassen’s algorithm • Closest pair problem
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- 31. 14 23 45 98 6 33 42 67
- 32. Merge 23 45 98 33 42 6714 6
- 33. Merge 23 45 98 6 42 67 6 14 33
- 34. Merge 14 45 98 6 42 67 6 14 23 33
- 35. Merge 14 23 98 6 42 67 6 14 23 45 33
- 36. Merge 14 23 98 6 33 67 6 14 23 33 45 42
- 37. Merge 14 23 98 6 33 42 6 14 23 33 42 45 67
- 38. Merge 14 23 45 6 33 42 6 14 23 33 42 45 98 67
- 39. Merge 14 23 45 98 6 33 42 67 6 14 23 33 42 45 67
- 40. Merge 14 23 45 98 6 33 42 67 6 14 23 33 42 45 67 98
- 42. QUICKSORT (A, p, r) 1. if p < r 2. q = PARTITION (A, p, r) 3. QUICKSORT (A, p, q-1) 4. QUICKSORT (A, q -1, r) Partitioning the array PARTITION (A, p, r) 1. X=A[r] 2. i =p -1 3. for j = p to r -1 4. if A[j] X 5. i = i + 1 6. exchange A[i] with A[j] 7. exchange A[i+1] with A[r] 8. return i+1